A popular method to address model uncertainty is model selection, which picks the “best” model based on certain data-driven criteria, e.g., information criteria. Traditional model selection methods have been extended to SIMs, such as AIC [1]} and cross-validation [2]}. More recently, [3]} studied a shrinkage-type estimator to select and estimate covariates in SIMs.
As an alternative to model selection, model averaging (MA) addresses model uncertainty by combining estimators from all candidate models with certain weights based on the model performance, and it often leads to lower risk than model selection [4]}.
The past decade has witnessed burgeoning literature pertaining to model averaging. There are two main streams of averaging techniques: Bayesian model averaging (BMA) and frequentist model averaging (FMA). Although BMA is flexible and can be applied in many models, the choice of prior probabilities is often challenging and experiential [5]}. There are various FMA methods, and a partial list includes smoothed information criteria [6]}, optimal averaging [7]}, adaptive combination [8]} and plug-in methods [9]}. Despite the increasing popularity of the averaging techniques, MA estimators for SIMs are hardly studied.
